The reaction sun drum brake band is applied in 1st and 2nd gear and is released in Park, Reverse, Neutral, 3rd and 4th gear. Since you have motion in Reverse, 3rd and 4th gears there is a possibility the brake band is slipping or the hydraulically operated piston that applies the brake band is not working.
It is also possible the 2-3 shift solenoid (Shift B) is defective and won't energize for 1st and 2nd gear operation. However, a defective solenoid should produce a CEL and a Check Trans indication. You can replace the solenoid without removing the transmission, you have to disassemble the transmission to replace the band.
The 1-2/3-4 shift solenoid (shift A) is energized in Winter Mode and is working because 3rd is available, the 2-3 shift solenoid (Shift B) is de-energized in 3rd and 4th which typically would be the failure state.
02 Rodeo Sport 4X4 3.2L V6
01 Rodeo Sport 4X4 3.2L V6